Editing Curry's paradox (section)

=== Informal proof===

The standard method for proving [[conditional sentence]]s (sentences of the form "if ''A'', then ''B''") is called "[[conditional proof]]".   In this method, in order to prove "if ''A'', then ''B''", first ''A'' is assumed and then with that assumption ''B'' is shown to be true.

To produce Curry's paradox, as described in the two steps above, apply this method to the sentence "if this sentence is true, then Germany borders China".  Here ''A'', "this sentence is true", refers to the overall sentence, while ''B'' is "Germany borders China".  So, assuming ''A'' is the same as assuming "If ''A'', then ''B''". Therefore, in assuming ''A'', we have assumed both ''A'' and "If ''A'', then ''B''".  Therefore, ''B'' is true, by [[modus ponens]], and we have proven "If this sentence is true, then 'Germany borders China' is true." in the usual way, by assuming the hypothesis and deriving the conclusion.

Now, because we have proved "If this sentence is true, then 'Germany borders China' is true", then we can again apply modus ponens, because we know that the claim "this sentence is true" is correct. In this way, we can deduce that Germany borders China.